Method for using an atomic force microscope

ABSTRACT

The present invention relates to a method of using an atomic force microscope comprising exciting natural lower and higher vibration modes of a microlever (M) placed on a sample, and analyzing the variation of one variable of a first output signal (A i  cos(ω i t−φ i )) representative of the response of M to the excitation of the lower mode, with respect to the variation of a parameter influenced by one variable of a second output signal (A j  cos(ω j t−φ j )) representative of the response of M to the excitation of the higher mode, and/or analyzing the variation of one variable of a second output signal (A j  cos(ω j t−φ j )) representative of the response of M to the excitation of the higher mode, with respect to the variation of a parameter influenced by one variable of a first output signal (A i  cos(ω i t−φ i )) representative of the response of M to the excitation of the lower mode.

FIELD OF THE INVENTION

In general, this invention relates to a method of using an atomic forcemicroscope (AFM) by means of amplitude modulation in order to analyse asample at a nanometric scale, and, in particular, to a method of usingsaid AFM by the simultaneous excitation of several normal vibrationmodes of the microlever thereof.

PRIOR STATE OF THE ART

In the past few years, atomic force microscopy (AFM), in its dynamicmodes, has become one of the most powerful and versatile techniques forthe nanometric-scale characterisation of the topography of a largevariety of materials, such as biological molecules, polymers,semiconductors, ceramic materials or organic molecules. Due to theirvery high resolution (lateral and vertical) and robust operation, atomicforce microscopes have been incorporated into both research laboratoriesand innovation and characterisation departments in technologicalsectors, such as the development of polymers or integrated circuits, tomention two examples. The potential of AFM microscopies in both basicresearch and technological applications would considerably expand ifthey could detect very small forces, in the pN range. Thus, the highspatial resolution could be accompanied by a great capacity to measureother surface physical or chemical properties, such as the chemicalcomposition or the mechanical properties.

On the other hand, atomic force microscopy technology has led to a newtype of micro- and nanomechanical sensors based on the changes in thedynamic properties (amplitude, phase or frequency) undergone by amicrolever when chemical or biological molecules are adsorbed thereon(J. Fritz et al. Science 288, 316 (2000)).

The most widely spread AFM mode is known as amplitude modulation mode(AM-AFM; the most widespread commercial name is tapping mode AFM), whichconsists of the excitation of the microlever at the (fundamental)resonance frequency and the establishment of a feedback system based onthe monitoring of the oscillation amplitude.

Since 1993, various schemes have been proposed to combine topography andcompositional contrast using the dynamic modes of AFM. The mostnoteworthy has consisted of measuring the phase displacement between theoscillation signal and the excitation force. The measurement of thephase displacement is performed jointly and simultaneously with themeasurement of the amplitude. In this case, the phase has been proposedin order to obtain information about compositional variations (D.Chemoff, Proc. Microscopy and Microanalysis, New York 1996; J. Tamayoand R. Garcia, Appl. Phys. Lett. 71, 2394 (1997); J. P. Cleveland et al.Appl. Phys. Lett. 72, 2613 (1998); G. Bar et al. Langmuir 14, 7343(1998)). These measurements have made it possible to obtain images wherethe various components of polymer materials, semiconductors or organiccompounds are visualised. However, various works have shown that thephase signal pertaining to the oscillation is governed by the inelasticenergy dissipated between the tip and the sample. This suggests thatdifferent combinations of inelastic processes and elastic properties ofthe material may cause the same phase displacement; consequently, thephase displacement of the first harmonic does not provide quantitativeinformation about the properties of the material (Tamayo, García AppliedPhys. Letters 73, 2926 (1998)). On the other hand, it has been shownthat the phase signal also includes a topographic component, which makesseparation between topographic and compositional information moredifficult (M. Stark et al. Biophys. J. 80, 3009 (2001)).

Recently, other methods have been proposed to combine topographicinformation and chemical information, such as patent (P. Hinterdorfer,J. Nelson, U.S. Pat. 60/423,222); however, this type of schemes are onlyapplicable to measure specific interactions between biologicalmolecules, which considerably restricts the scope of application of themethod.

Several factors may contribute to explain the current limitations ofatomic force microscopy to obtain information beyond topography. Amongstthem, it is worth mentioning the consideration of the AFM microlever asa single-mode mechanical system, i.e. the microlever is considered to bea mechanical system characterised by a single resonance frequency (thefundamental one). Consequently, the excitation is performed atfrequencies close to the resonance frequency. However, a microlever hasseveral vibration modes, all of them at frequencies higher than thefundamental frequency. For example, for a lever in the shape of arectangular prism, with a uniform density, the ratio between frequenciesis ν₀, 6.39ν₀, 17.9ν₀. In atomic force microscopy, the contributions ofthe modes higher than the oscillation amplitude are quite small, butthey are, however, noticeable under experimental conditions (R.Hillenbrand et al. Appl. Phys. Lett. 76, 3478 (2000); Stark T. R.Rodríguez, R. García, Appl. Phys. Lett. 80, 1646 (2002)).

In order to increase the higher mode components, the simultaneousexcitation of several oscillation modes of the microlever has beenproposed (T. R. Rodríguez, R. García, PCT/ES2006/070016 and Appl. Phys.Lett. 449, 84 (2004).

The final result entails having a microscope that has 2n independentinteraction channels with the material (two for each vibration mode),each of which could analyse a different property.

Application PCT/ES2006/070016 proposes a method of using an atomic forcemicroscope by means of amplitude modulation, which comprises excitingtwo natural vibration modes of the microlever, and analysing thevariation of the oscillation amplitude of the microlever's response tothe excitation in the lower mode, in order to obtain topographicinformation about the sample, and analysing the phase variation, orphase displacement, of the microlever's (M) response to the excitationin the higher mode, in order to obtain compositional information aboutthe sample.

In this application, said variations are analysed with respect to thetotal oscillation amplitude of the microlever, both that of theamplitude of the lower mode (as was conventionally done) and that of thephase, or phase displacement, of the higher mode, and it is shown that,for changes in the properties of the sample material, the phasevariation, or phase displacement, in the higher mode is significant,contrary to what occurs with the lower mode, which justifies saidproposal, in the sense of using the variation of amplitude of the lowermode, or first mode, with respect to the variation of said totalamplitude to obtain topographic information about the sample and thevariation of the phase of the higher mode, with respect to the totalamplitude, to obtain information about the compositional contrast of thesample, or of different samples.

Although said proposal represented a great advance in the field ofatomic force microscopy, by assuming the microlever's multi-modecharacter, and was able to significantly increase the sensitivity ofsuch microscopes to compositional contrast, said proposal still carriesone of the limitations of conventional methods; namely, performing theanalyses of the variations of the variables with respect to the totaloscillation amplitude of the microlever's response, both in regards tothe conventional use of the amplitude of the lower mode as the variableto be analysed, and the proposed use, in said applicationPCT/ES2006/070016, of the phase of the higher mode as the variable to beanalysed.

EXPLANATION OF THE INVENTION

These inventors have observed that, starting from the advantagesobtained upon assuming the microlever's multi-mode character, as done inapplication PCT/ES2006/070016, but eliminating the limitations describedabove, it is possible to increase the sensitivity of an atomic forcemicroscope even further, as well as not limit the use of the amplitudeof the lower mode to obtain topographic information, nor that of thephase of the higher mode for the compositional information.

To do so, this invention relates to a method of using an atomic forcemicroscope by means of amplitude modulation, of the type that comprisesexciting, normally in a simultaneous manner, at least one natural lowervibration mode and one natural higher vibration mode of a microlever ofsaid microscope, placed on a sample to be examined.

The proposed method comprises:

-   -   analysing at least the variation of one variable of a first        output signal that is representative of the response of said        microlever to said excitation of said lower mode, with respect        to the variation of at least one parameter which is influenced        by one variable of a second output signal that is representative        of the response of said microlever to said excitation of said        higher mode,

and/or

-   -   analysing at least the variation of one variable of a second        output signal that is representative of the response of said        microlever to said excitation of said higher mode, with respect        to the variation of at least one parameter which is influenced        by one variable of a first output signal that is representative        of the response of said microlever to said excitation of said        lower mode.

For a preferred embodiment example, said lower mode is the microlever'sfirst natural vibration mode and said higher mode is the microlever'ssecond natural vibration mode.

Although, preferably, said parameter or parameters are equivalent to thevariable whereby they are influenced, in another embodiment example, atleast one of said parameters is influenced, in a weighted manner, by atleast two variables of, respectively, a first and a second output signalthat are representative of the response of said microlever to,respectively, said excitation of said lower mode and said higher mode.

In general, said variables that influence said parameters are relativeto the oscillation amplitude.

Depending on the embodiment example, said variable of said first outputsignal and said variable of said second output signal are each relativeto the oscillation amplitude, to the phase or to the resonance frequencyof their respective output signals.

Specifically, in order to perform said analysis or analyses, the methodcomprises using, for different embodiment examples:

-   -   the phase as the variable of said first output signal, and the        amplitude as the variable of said second output signal, or        viceversa,    -   the amplitude as the variable of said first output signal, and        the resonance frequency as the variable of said second output        signal, or viceversa,    -   the phase as the variable of said first output signal, and the        resonance frequency as the variable of said second output        signal, or viceversa,    -   the amplitude as the variable of both output signals,    -   the phase as the variable of both output signals,    -   the resonance frequency as the variable of both output signals.

For another embodiment example, the method comprises exciting one ormore higher modes of the microlever, and taking into account, for saidanalysis or analyses, one or more variables of an output signal obtainedby said excitation of said other higher mode.

The proposed method comprises performing the analyses described toobtain topographic and/or compositional information about said sample,without limiting the use of the variation of the amplitude of the lowermode to obtain topographic information, nor that of the phase of thehigher mode to obtain compositional information, as proposed inapplication PCT/ES2006/070016, but any of the variables described abovefor the different embodiment examples, i.e. the amplitude, the phase orthe frequency of any of the modes, with respect to an equivalentparameter or one that is influenced at least in part by the amplitude,the phase or the frequency of another mode, in any order.

The proposed method also comprises changing said sample to be examinedby, at least, a second sample and performing, with said second sample,the same steps that were performed with the sample.

In order to facilitate the interpretation and presentation of theresults of the analyses described, the method comprises performing across-representation of the data obtained as a result of said analysisor analyses, for two or more variables of, respectively, two or moreoutput signals that are representative of the response of saidmicrolever to corresponding excitations of said natural vibration modes.

For an embodiment example, said representations are visualrepresentations, in the form of a graph or a table, some of which arerepresented in the attached figures, which will be described in asection below.

The method also comprises recording and classifying the data obtainedfor a plurality of different samples, as well as comparing the dataobtained for an analysis of the sample located under said microlever tosaid recorded data, and, on the basis of the result of said comparison,establishing a degree of similarity with at least one sample of saidplurality of samples.

BRIEF DESCRIPTION OF THE DRAWINGS

The preceding and other advantages and characteristics will be morefully understood from the following detailed description of someembodiment examples that refer to the attached drawings, which arepresented for illustrative, non-limiting purposes, and wherein:

FIG. 1 shows a block-level description of an atomic force microscope asthat proposed by application PCT/ES2006/070016, but with a number ofadded blocks, framed within dotted lines, which are used to perform themethod proposed by this invention.

FIG. 2 is a graph that shows, for two different materials, the variationof the phase displacement of the second oscillation mode of themicrolever when it is excited in the first two modes (with freeoscillation amplitudes of 10 and 1 nm, respectively), with respect tothe amplitude of the first mode.

FIG. 3 is a graph that shows, for two different materials, the variationof the phase displacement of the first oscillation mode of themicrolever when it is excited in the first two modes (with freeoscillation amplitudes of 10 and 1 nm, respectively), with respect tothe amplitude of the second mode.

FIG. 4 is a graph that shows, for two different materials, the variationof the phase displacement of the first oscillation mode of themicrolever when it is excited in the first two modes (with freeoscillation amplitudes of 10 and 1 nm, respectively), with respect tothe amplitude of the first mode.

FIG. 5 is a graph that shows, for two different materials, the variationof the phase displacement of the second oscillation mode of themicrolever when it is excited in the first two modes (with freeoscillation amplitudes of 10 and 1 nm, respectively), with respect tothe amplitude of the second mode; and

FIG. 6 is a graph that shows, for two different materials, the variationof the phase displacement of the second oscillation mode of themicrolever when it is excited in the first two modes (with freeoscillation amplitudes of 10 and 1 nm, respectively), with respect to aparameter that is representative of a weighted sum of amplitudes of bothmodes.

DETAILED DESCRIPTION OF SOME EMBODIMENT EXAMPLES

A number of experimental simulations and trials have been performed inorder to demonstrate the value of the proposed method, which, amongstothers, have offered a number of data that are represented by the graphsillustrated by FIGS. 2 to 6.

Below we explain a number of concepts and mathematical expressionswherein the above-mentioned simulations have been based, which explainthe behaviour of the microscope illustrated by FIG. 1, used inaccordance with the proposed method.

As mentioned above, this invention assumes the multi-mode character ofmicrolever M (see FIG. 1), the simultaneous excitation of several modesof microlever M by mechanical, electrostatic or thermal means, or anycombination thereof. This invention specifies that what is relevant toobtain an increase in the sensitivity of the micromechanical device(atomic force microscope or mechanical sensor) to physical interactionsin the use of analyses and representations that cross parameters fromone mode (amplitude, phase or resonance frequency) with parameters fromanother mode (cross-representations).

The feasibility of the invention is based on the numerical analysis ofthe dynamic behaviour of an atomic force microscope, a task that hasbeen performed at the Forces and Tunnel laboratory of the Higher Councilfor Scientific Research (CSIC).

In the first place, microlever M is considered to be a continuoussystem, w(x,t), that is externally excited and interacts with the samplethrough a long-range interaction (van der Waals force) and a short-rangeinteraction described by the Derjaguin-Muller-Toporov model. Under theseconditions, the equation of movement is:

$\begin{matrix}{{{\frac{EI}{L^{4}}{\frac{\partial^{4}}{\partial x^{4}}\left\lbrack {w\left( {x,t} \right)} \right\rbrack}} + {a_{1}\frac{\partial{w\left( {x,t} \right)}}{\partial t}} + {{bh}\; \rho \frac{\partial^{2}}{\partial x^{2}}{w\left( {x,t} \right)}}} = {F_{exc} + F_{med} + F_{ts}}} & \text{-1-}\end{matrix}$

where E is Young's module, I is the moment of inertia formed bymicrolever M, and L is the length. F_(exc), F_(med) and F_(ts) are,respectively, the excitation force, the friction force with the mediumand the interaction force per unit of length.

On the other hand, the deflection of microlever M is expressed as:

$\begin{matrix}{{w\left( {L,t} \right)} = {{\sum\limits_{n = 1}^{\infty}{{\phi_{n}(L)}{Y_{n}(t)}}} = {{\sum\limits_{n = 1}^{\infty}{y_{n}(t)}} = {{y_{1}(t)} + {y_{2}(t)} + {y_{3}(t)} + \ldots}}}} & \text{-2-}\end{matrix}$w(L,t)=y ₀ +A ₁ cos(ω₁ t−φ ₁)+A ₂ cos(ω₂ t−φ ₂)+A ₃ cos(ω₃ t−φ ₃)+  -3-

where,

y _(i) =A _(i) cos(ωt−φ _(i))  -4-

The total amplitude (rms value) would be calculated as

$\begin{matrix}{A_{tot} = \left\lbrack {\frac{2}{T}{\int_{0}^{T_{n}}\ {{t\left\lbrack {w\left( {L,t} \right)} \right\rbrack}^{2}}}} \right\rbrack^{1/2}} & \text{-5-}\end{matrix}$

The different channels arise naturally when microlever M of an AFM isconsidered to be a mechanical system that contains many autovibrationmodes. The excitation of the first mode and the non-linear character ofthe interaction generate the excitation of higher harmonics of the firstmode; however, it has been shown that the amplitude of these componentsunder relevant experimental conditions is approximately four orders ofmagnitude smaller than the fundamental one, which makes the experimentaluse thereof very difficult (T. R. Rodríguez, R. García, Appl. Phys.Lett. 80, 1646 (2002)). In order to increase the higher mode components,the simultaneous excitation of several oscillation modes of microlever Mhas been proposed, which may be two, three, four, etc. (R. García and T.R. Rodríguez, PCT/ES2006/070016). The purpose is to establish arelationship between the amplitudes of the lowest frequency mode and thehigher mode of approximately 1%-10%. The excitation could also bemulti-mode by means of an expression of the type,

$\begin{matrix}{{F_{exc}\left( {x,t} \right)} = {\sum\limits_{i}^{n}{F_{i}\cos \; \omega_{i}t}}} & \text{-7-}\end{matrix}$

where F_(i) and ω_(i) represent the excitation force and the modefrequency of microlever M. As a consequence of this previous excitation,2n communication channels with the sample will be generated. For eachmode, two channels are provided, one for amplitude A and the other forphases φ. For reasons of brevity and in order to show the concept ofmulti-mode operation, we will present the two-mode case of the atomicforce microscope, i.e. when two vibration modes are simultaneouslyexcited, which may be the first and the second, the first and the third,and so on, or the second and the third, etc., and all the possiblecombinations between them. The two-mode excitation is as follows:

F _(exc)(x,t)=F _(i) cos ω_(i) t+F _(j) cos ω_(j) t  -8-

where ω_(i) and ω_(j) are the frequencies of two normal modes ofmicrolever M that fulfil the condition j>i. Thus, the amplitude of thehigher modes will no longer be simply controlled by the excitationcaused by the harmonics of the fundamental mode, as is the case with a(dynamic) atomic force microscope, but as a result of a force that maybe controlled by the observer.

The microscope illustrated by FIG. 1 is like that proposed in patentapplication PCT/ES2006/070016, with the corresponding two-modeexcitation module, formed by the AFM control unit and the two-modecontrol unit, already described in said application, as well as a numberof added blocks, framed within dotted lines, which are used to performthe method proposed by this invention.

One of said blocks is adapted to perform the analyses described above,at least in part, as well as the cross-representations also describedabove.

The other module indicated with dotted lines in FIG. 1 is thatpertaining to the feedback of scanner z, i.e. the sample support, whichgenerally consists of a piezoelectric tube controlled by a feedbackmechanism designed to adjust the distance between the tip of microleverM and the sample, in order to maintain a constant force between them.

Said feedback mechanism conventionally only takes into consideration theamplitude of the first mode, i.e. A_(i), but the method proposed by thisinvention comprises performing said feedback on the basis not only ofthe amplitude of the first mode, A_(i), but also of the total amplitude,A_(tot).

Said FIG. 1 represents the excitation signal of the lower mode as F_(i)cos ω_(i)t, and that of the higher mode as F_(j) cos ω_(j)t, with j>i.

For a preferred embodiment example, the proposed method comprisesperforming both excitations by means of a single excitation signal F_(i)cos ω_(i)t+F_(j) cos ω_(j)t, composed of the sum of said two excitationsignals F_(i) cos ω_(i)t and F_(j) cos ω_(j)t, and, as indicated by anarrow in FIG. 1, applied to microlever M.

For an embodiment example, the method comprises performing theexcitation of the two modes externally, and, for another embodimentexample, the method comprises performing the excitation of one of saidmodes externally, and the excitation of the other mode or modes byself-excitation by harmonics or sub-harmonics of the externalexcitation.

Said external excitation may be any of the following excitations:mechanical, thermal, electrostatic or a combination thereof.

The method also comprises, as shown in FIG. 1, breaking down an outputsignal A_(i) cos(ω_(i)t−φ_(i))+A_(j) cos(ω_(j)t−φ_(j)), which isrepresentative of the response of said microlever M to said excitationby said compound excitation signal F_(i) cos ω_(i)t+F_(j) cos ω_(j)t,separating the parts of the signal that correspond to the response toeach of said two excitations, and subsequently using the variablesthereof to perform the above-mentioned analyses.

Specifically, the method comprises breaking down (as was done in theproposal of application PCT/ES2006/070016) the information contained insaid output signal A_(i) cos(ω_(i)t−φ_(i))+A_(j) cos(ω_(j)t−φ_(j)) intofour channels: two channels with information about oscillation amplitudeA_(i), A_(j) of said output signal A_(i) cos(ω_(i)t−φ_(i))+A_(j)cos(ω_(j)t−φ_(j)) for said two excitation frequencies, and two channelswith information about phase φ_(i), φ_(j) of said output signal A_(i)cos(ω_(i)t−φ_(i))+A_(j) cos(ω_(j)t−φ_(j)) for said two excitationfrequencies.

Said four channels are used to perform the analyses andcross-representations in accordance with the method proposed by thisinvention, some of which are illustrated by FIGS. 2 to 6, for some ofthe possible embodiment examples presented in a previous section.

The numerical simulations presented below illustrate the advantagesoffered by the analysis and the cross-representation of variablespertaining to different modes, in the particular case of a two-modeexcitation that acts on the first and second modes of an AFM.

FIG. 2 shows how the dependency of the phase of the second mode φ₂ withrespect to the amplitude of the first mode A₁ makes it possible todistinguish between two different interaction forces; that is, twodifferent materials (it may be observed that, for A₁=5 nm, there is avariation of Δφ₂=3 degrees, which the model allows to convert into anincrease in interaction forces that in this case is equal to ΔF=3.41pN), the Hamacker constants whereof are H=4.7×10⁻²⁰ J and H=9×10⁻²⁰ J,respectively. This analysis, the result whereof has been graphicallyrepresented in said FIG. 2, makes it possible to detect the differencesbetween the materials.

FIG. 3 shows how the dependency of the phase of the first mode φ₁ withrespect to the oscillation amplitude of the second mode A₂ makes itpossible to distinguish between two different interaction forces; thatis, two different materials (it may be observed that, for A₂=0.8 nm,there is a variation of Δφ₁=10 degrees, which the model allows toconvert into an increase in interaction forces that in this case isequal to ΔF=21.70 pN), which are represented in FIG. 2. This analysis,the result whereof has been graphically represented in said FIG. 3, alsomakes it possible to detect the differences between the materials.

FIG. 4 shows that the phase of the first mode φ₁ is not sensitive to thechange in material properties (only elastic interactions are considered)when it is represented with respect to its own amplitude A₁. Thisrepresentation does not make it possible to detect the differencesbetween the materials.

FIG. 5 shows that the phase of the second mode φ₂ is not sensitive tothe change in material properties (only elastic interactions areconsidered in the model) when it is represented with respect to its ownamplitude A₂. This representation does not make it possible to detectthe differences between the materials.

The results shown in FIGS. 4 and 5 are in contrast with those obtainedin FIGS. 2 and 3.

The results shown in FIGS. 2-5 have been obtained with the followingparameters L, b, h, E, R and ρ for 255 nm, 40 nm, 1.8 nm, 170 GPa, 20 nmand 2,320 kg/m2; k1=0.9 N/m, k2=35.22 N/m; Q1=255; Q2=1,002; F1=60 pNand F2=20 pN. The two materials used were simulated using Hamackerconstants Ha=4.7×10⁻²⁰ J and Hb=9×10⁻²⁰ J.

The preceding figures have allowed to establish that the most genuineway to obtain compositional contrast by attractive elastic interactionsis the analysis and cross-representation of variables of both modes. Ifthe phase of one mode is represented with respect to its own amplitude,no contrast is obtained (in the absence of elastic interactions).

In the embodiment examples illustrated by FIGS. 2 and 3, the abcissaaxis represents a pure variable of one mode, specifically, the amplitude(A₁ in FIG. 2 and A₂ in FIG. 3). These cases are representative of theembodiment examples described for which the parameter, or theparameters, with respect to which the variation analysis of a variableis performed (φ₂ in FIG. 2 and φ₁ in FIG. 3) are equivalent to a singlevariable, in this case A₁ in FIG. 2 and A₂ in FIG. 3.

Other embodiment examples are proposed, also already described, forwhich said parameters are influenced, in a weighted manner, by twovariables of, respectively, a first A_(i) cos(ω_(i)t−φ_(i)) and a secondA_(j) cos(ω_(j)t−φ_(j)) output signals that are representative of theresponse of microlever M to, respectively, the excitation of the lowermode and of the higher mode.

FIG. 6 is representative of said embodiment examples for which saidparameters are a weighted sum of amplitudes of both modes. Thedifferences between the graphs of both materials (the same as in FIGS. 2to 5), it is also possible to maintain the sensitivity to the change ininteraction forces if the variable of one mode (amplitude or phase) isrepresented with respect to said parameter that is representative of aweighted sum of amplitudes of both modes, which, for said embodimentexample illustrated in FIG. 6, are the total amplitude (rms value), butwhich for other embodiment examples could be any other type of weightedsum.

The proposed method is equally applicable for those cases whereinmicrolever M is used as a sensor to determine the adsorption of chemicalor biological molecules.

For an embodiment example of the proposed method, either the amplitudeof the lower mode A_(i) or the total amplitude is used to form an imageof the system's topography, whereas the cross signals pertaining todifferent modes A_(j) and φ_(j) are used to complete the topographiccharacterisation or to provide information about the material's physicaland/or chemical properties, in the form A_(j) vs. φ_(j), or φ_(j) vs.φ_(i), φ_(i) vs. A_(j), with i≠j. The case φ_(i) vs. A_(tot), whereφ_(i) is the phase of a mode other than the fundamental one, could alsobe considered.

A person skilled in the art could introduce changes and modifications inthe embodiment examples described without going beyond the scope of theinvention, as defined in the attached claims.

1. A method of using an atomic force microscope by means of amplitudemodulation, the method comprising the steps of: exciting at least onenatural lower vibration mode and one natural higher vibration mode of amicrolever of said atomic force microscope, analysing at least one of avariation of one variable of a first output signal that isrepresentative of a response of said microlever to said excitation ofsaid lower vibration mode, with respect to a variation of at least oneparameter which is influenced by one variable of a second output signalthat is representative of a response of said microlever to saidexcitation of said higher vibration mode, and a variation of onevariable of the second output signal that is representative of aresponse of said microlever to said excitation of said higher vibrationmode, with respect to a variation of at least one parameter which isinfluenced by one variable of a first output signal that isrepresentative of a response of said microlever to said excitation ofsaid lower vibration mode.
 2. The method of claim 1, wherein at leastone of said at least one parameters is equivalent to said one variableby which it is influenced.
 3. The method of claim 1, wherein at leastone of said at least one parameters is influenced, in a weighted manner,by at least two variables of, respectively, the first and the secondoutput signals that are representative of the response of saidmicrolever to, respectively, said excitation of said lower vibrationmode and of said higher vibration mode.
 4. The method of claim 1,wherein the variable of said first output signal and said variable ofsaid second output signal are each relative to at least one of anoscillation amplitude, a phase and a resonance frequency of therespective first and second output signals.
 5. The method of claim 4,wherein said influencing variable or variables of at least one of saidparameters are relative to the oscillation amplitude.
 6. The methodclaimed in of claim 4, wherein the analysis step comprises using: aphase as the variable of said first output signal and an amplitude asthe variable of said second output signal; or an amplitude as thevariable of said first output signal and an resonance frequency as thevariable of said second output signal; or the phase as the variable ofsaid first output signal and the resonance frequency as the variable ofsaid second output signal; or the amplitude as the variable of bothoutput signals, or the phase as the variable of both output signals, orthe resonance frequency as the variable of both output signals.
 7. Themethod of claim 1, wherein said lower vibration mode is a first naturalvibration mode of the microlever.
 8. The method of claim 1, wherein saidhigher vibration mode is a second natural vibration mode of themicrolever.
 9. The method of claim 1, further comprising the step ofexciting at least another higher vibration mode of the microlever, andwherein said analysis steps further include at least one variable of anoutput signal obtained by said excitation of said other higher vibrationmode.
 10. The method of claim 1, wherein it comprises performing saidexcitation of at least said two modes externally.
 11. The method ofclaim 1, further comprising the steps of performing an excitation of oneof said modes externally, and performing the excitation of the othermode by one of self-excitation, harmonics, and sub-harmonics of theexternal excitation.
 12. The method of claim 10, wherein said externalexcitation is at least one excitation from the group that includesmechanical, thermal, electrostatic, and a combination thereof.
 13. Themethod of claim 1, further comprising the step of performing saidanalysis or analyses to obtain at least one of topographic andcompositional information about said sample.
 14. The method of claim 13,wherein further comprising the steps of changing said sample to beexamined by at least one second sample, and performing, with said secondsample, the same steps that were performed with the first sample. 15.The method of claim 1, wherein further comprising the step of performingat least one cross-representation of the data obtained as a result ofsaid analysis step, for two or more variables of, respectively, two ormore output signals that are representative of the response of saidmicrolever to the corresponding excitations of said natural vibrationmodes.
 16. The method of claim 15, wherein said cross-representation isa visual representation, in the form of a graph or a table.
 17. Themethod of claim 14, wherein further comprising the steps of recordingand classifying the data obtained for a plurality of different samples.18. The method of claim 17, further comprising the steps of: comparingthe data obtained for an analysis of the sample located under saidmicrolever to said recorded data, and establishing, based on thecomparison, a degree of similarity with at least one sample of saidplurality of samples.
 19. The method of claim 1, further comprising thestep of performing at least two of said excitations of said naturalvibration modes of the microlever simultaneously.
 20. The method ofclaim 19, wherein performing said excitations using compound excitationsignal composed of the sum of said two excitation signals.
 21. Themethod of claim 20, wherein further comprising the steps of: breakingdown a compound output signal that is representative of the response ofsaid microlever to said excitation using said compound excitationsignal; separating the compound output signal into parts that correspondto the response to each of said excitations, which are at least two, andsubsequently using the variables thereof to perform at least theabove-mentioned analyses.